The Paris Agreement has motivated studies on the consequences of limiting global warming to the target 1.5°C and 2°C levels above pre-industrial conditions. It is challenging to quantify changes across a small increment of global warming, so a pattern-scaling approach may be considered. In our analysis, we investigate the linearity of local temperatures from a 1.5°C world up to a 2°C world. Ensembles of transient coupled climate simulations from multiple models under different scenarios were compared and individual model responses were analyzed. For many places, the multi-model ensemble average suggests that a linear warming response is likely. However, individual model results vary and large contributions from non-linear changes in unforced variability or the forced response cannot be ruled out. In some regions, such as East Asia, models simulate an acceleration in local warming from a 1.5°C world up to a 2°C world. Examining East Asia during boreal summer, we find increased warming in the simulated 2°C world relative to scaling up from 1.5°C is related to reduced anthropogenic aerosol emissions. Our findings suggest that, where forcings other than those due to greenhouse gas emissions change, the warming experienced in a 1.5°C world is a poor predictor for local climate at 2°C of global warming.